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Aim

A quick search for .

Question

If $|f(z) |\leq 1 + |z|$, show that $f(z) = az + b$ is a recently-posted question. I tried to search for its duplicates on Approach0 but I didn't manage to get something like Showing that $f$ is linear function if $\forall z \in \mathbb{C}$, $|f(z)| \leq 1 + |z|$..

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How can I search for dupes of this question on the main site and/or Approach0?

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    $\begingroup$ Interestingly, if I take the search you linked and omit all occurrences of \left... and \right.... then it appears near the top. I am not sure whether this should make much difference - I have asked about this in the searching chatroom. $\endgroup$ Nov 26 '20 at 10:56
  • $\begingroup$ @MartinSleziak Thanks for comment. The left and right are automatically generated by the search page's input text field/area. $\endgroup$ Nov 26 '20 at 11:10
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    $\begingroup$ I see. I only use the "raw query" to input formulas in Approach0. (Either by directly entering/editing LaTeX, or by copy-paste - and I have a bookmarklet to make copy-paste faster.) So I have no experience with entering a math formula with that editor which is used there. $\endgroup$ Nov 26 '20 at 11:15
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    $\begingroup$ I think finding the right search terms is as much an art as a science. After trying a few other things, I found that searching on math.stackexchange for "linear function" [complex-analysis] got me the duplicate. (The [complex-analysis] restricts the search to questions tagged complex-analysis.) $\endgroup$ Nov 26 '20 at 11:23
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    $\begingroup$ @GNUSupporter8964民主女神地下教會 A0 author here. As MartinSleziak pointed out, you need to strip those \left and \right around "vertical bar" to find that post. I did not find a good way to parse vertical bars used in representing absolute values if they do not have \left \right to help me parse, what I do is simply treat a single bar as a leaf token. That is why you see the difference as in original post it does not have \left \right surrounded, and you need to use the same representation in your query to find that post. $\endgroup$
    – Wei Zhong
    Nov 27 '20 at 3:23
  • $\begingroup$ @WeiZhong Thanks for your answer. Lemme write a "solution" when I've time now so that this question is treated as resolved. $\endgroup$ Nov 27 '20 at 7:24
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For the MathSE built-in search: as non-MathJax is detected more accurately we can use some of the content in the body of the post to aid our search.

So for example: \leq "integral formula" gives around 350 results and fine-tuning to "f(z)" \leq "integral formula" yields 223. We can also try variants like \le in place of \leq which interestingly gives fewer hits.

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Probably this question was asked partly due to the fact that the post did not appear in the search results in Approach0. The reason is that this search engine differentiates between \left|...\right| and |....|. (On the other hand, \left(...\right) or \left{...right} are treated the same as (...) or {...}. In this case, the shape of the bracket already indicates whether it is left or right bracket.

This is mentioned also in the entry of How to search on this site? which deals with Approach0 (current revision - see the last paragraph). More details can be found in chat, for example, here and here.

In particular, this is the search query linked in the question - and here is the same query where \left|...\right| was replaced by |....|. The question Showing that $f$ is linear function if $\forall z \in \mathbb{C}$, $|f(z)| \leq 1 + |z|$ is among the top results only for the latter query.

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  • $\begingroup$ This answer basically summarizes what was said in the comment and in chat. I have made it CW, feel free to edit it further if there is something to add/improve. $\endgroup$ Dec 2 '20 at 9:23

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